Calculation Of Area In surveying By Simpson Rule

Calculation of Areas in Surveying | Simpson’s

Rule

In one of my previous articles, I discussed

Midpoint Ordinate Rule and Average Ordinate

Rule in detail with an example and listed out

various important methods used for the

calculation of areas in Surveying. In this article,

we will deal with the next important method

(rule) i.e. Simpson’s Rule along with a numerical

example used for the calculation of areas in the

field of Surveying.

Here are the five important rules (Methods) used

for the calculation of areas in Surveying:

1. Midpoint ordinate rule

2. Average ordinate rule

3. Simpson’s rule

4. Trapezoidal rule

5. Graphical rule

Simpson’s Rule

Statement

It states that, sum of first and last ordinates has

to be done. Add twice the sum of remaining odd

ordinates and four times the sum of remaining

even ordinates. Multiply to this total sum by 1/3 rd

of the common distance between the ordinates

which gives the required area.

Where O1, O2, O3, …. O n are the lengths of the

ordinates

d = common distance

n = number of divisions

Note:

This rule is applicable only if ordinates are odd,

i.e. even number of divisions.

If the number of ordinates are even, the area of

last division maybe calculated separated and

added to the result obtained by applying

Simpson’s rule to two remaining ordinates.

Even if first or last ordinate happens to be zero,

they are not to be omitted from Simpson’s rule.

The following offsets are taken from a chain line

to an irregular boundary towards right side of the

chain line.

Chainage 0 25 50 75 100 125 150

Offset ‘m’ 3.6 5.0 6.5 5.5 7.3 6.0 4.0

Common distance, d = 25m

Area = d/3[(O 1+O 7) + 2 (O 3+O 5)+4(O 2+O4+O 6)]

= 25/3[(3.6+4)+2(6.5+7.3)+4(5+5.5+6)]

Area = 843.33sqm

Physical Survey or As-in-built Surveying

Physical Survey or As-Built survey.

As-built survey : a survey that documents the location of recently constructed elements of a construction project. As-built surveys are done for record, completion evaluation and payment purposes. An as-built survey is also known as a 'works as executed survey'. As built surveys are often presented in red or redline and laid over existing plans for comparison with design information.
The purpose of the As-Built Survey – also commonly called a Physical Survey – is to show the property “as it is built” at a particular point in time. While a pre-construction survey is performed to document conditions prior to construction work being performed, the As-Built survey is conducted to show the current state of the site at various stages throughout the duration of a project. It also serves as a close-out document to verify that the work authorized was completed to plans and in compliance with all relevant standards and regulations.
An As-built survey builds upon the base map of a project and includes research at local agencies, ground-level topography data, and the documentation of visible site improvements. The advantage of this survey is that the new Base Map can be updated to show the current conditions of the site.
As-Built Survey or Design Survey
Professional surveyors can customize the As-Built survey to suit clients’ needs. An As-built survey can be basic and depict only the level of detail the client requires for a specific phase of the project. Alternatively, the client may request a higher level of detail with elevations and contours, street cross sections, and detailed sketches of sewer and storm drain depths and pipe sizes.
The As-Built survey can be expanded to a more comprehensive Design Survey, which includes mapping of existing underground utilities based on review of agency and service provider documentation. This survey is detailed enough to be used for civil design purposes by engineers or architects throughout development.
This provides clients with accurate As-Built surveys that show exactly what has been completed by a certain date. This can be a valuable project management tool to adjust construction schedules as required and can also be used to plan subcontractor work schedules and payments.
PROFESSIONAL SURVEYORS can provide the full range of surveying services that may be required at various times during construction PROJECTS.

Hydrographic Or Bathymetric Surveying

Hydrographic surveying or bathymetric surveying is the survey of physical features present underwater. It is the science of measuring all factors beneath water that affect all the marine activities like dredging, marine constructions, offshore drilling etc.
Hydrographic surveying is mainly conducted under authority concerns. It is mainly carried out by means of sensors, sounding or electronic sensor system for shallow water.
The information obtained from hydrographic surveying is required to bring up nautical charts which involves,
Available depths
Improved Channels
Breakwaters
Piers
The aids to navigation harbor facility
These survey also take part in necessary data collection relating to construction and developments of port facilities, such as pier construction. This help in finding the loss in capacity due to silt and many uncertainties.
Applications of Hydrographic Surveying
Following are the applications of hydrographic surveying:
Dock and Harbor Engineering
Irrigation
River Works
Land reclamation
Water Power
Flood Control
Sewage Disposal
Uses of Hydrographic Surveying
Uses of hydrographic surveying are given below:
1. Depth of the bed can be determined
2. Shore lines can be determined
3. Navigation Chart Preparation
4. Locate sewer fall by measuring direct currents
5. Locating mean sea level
6. Scouring, silting and irregularities of the bed can be identified
7. Tide measurement
8. River and stream discharge measurement
9. Massive structures like bridges, dams harbors are planned.
Sounding in Hydrographic Survey
The process of determining depth below water surface is called as sounding. The step before undergoing sounding is determining the mean sea level. If the reduced level of any point of a water body is determined by subtracting the sounding from mean sea level, hence it is analogous to levelling.
The specific need for sounding are
1. Preparation of navigation charts that is an all-time information for future purpose also
2. Material that to be dredged has to be determined early to facilitate easy movement in project without any confusion
3. Material dredging should also accompany where filling has to be done. Material dumping is also measured
4. Design of backwaters, sea wells require detailed information that is obtained from sounding
Equipment for Sounding
The essential equipment used for undergoing sounding are
1. Shore signals and buoys
2. Sounding Equipment
3. Instruments for measuring angles.

Uses Of Geodimeter

Geodimeter
Geodimeter is an instrument which works based on the propagation of modulated light waves, was developed by E. Bergestand of the Swedish Geological Survey in collaboration with the manufacturer M/s AGA of Swedish. The instrument is more suitable for night time observations and requires a prism system at the end of the line for reflecting the waves.

Advantages Of Digital Survey Equipments Over Conventional Equipments

Modern surveying instruments provides faster and more precise surveying than conventional instruments. Their types and uses are discussed in this article.
In conventional surveying, chain and tape are used for making linear measurements while compass and ordinary theodolites are used for making angular measurements. Leveling work is carried out using a Dumpy level and a leveling staff. With such surveying instruments, survey work will be slow and tedious.
Hence modern surveying instruments are becoming more popular and they are gradually replacing old surveying instruments such as compass and Dumpy level. With modern surveying instruments, survey work will be precise, faster and less tedious. Some of the modern surveying instruments are discussed in this article.
Modern Surveying Instruments and Their Uses
Following are the modern surveying instruments which are used for surveying:
Electronic Distance Measurement (EDM) Instruments
Total Station
Global Positioning System (GPS)
Automatic Level
1. Electronic Distance Measurement (EDM) Instruments
Direct measurement of distances and their directions can be obtained by using electronic instruments that rely on propagation, reflection and reception of either light waves or radio waves. They may be broadly classified into three types:
a. Infrared wave instruments
b. Light wave instruments
c. Microwave instruments
a. Infrared Wave Instruments
These instruments measure distances by using amplitude modulated infrared waves. At the end of the line, prisms mounted on target are used to reflect the waves. These instruments are light and economical and can be mounted on theodolites for angular measurements. The range of such an instrument will be 3 km and the accuracy achieved is ± 10 mm.
E.g. DISTOMAT DI 1000 and DISTOMAT DI 5

Surveyors play an integral role in land development, from the planning and design of land subdivisions.

Land surveying and its importance

Surveying and land surveying is the measurement and mapping of our surrounding environment using mathematics, specialized technology and equipment. Surveyors measure just about anything on the land, in the sky or on the ocean bed. They even measure polar ice-caps.

Land surveyors work in the office and in the field. In the field, they use the latest technology such as high order GPS, Robotic Total Stations ( Theodolites ), and aerial and terrestrial scanners to map an area, making computations and taking photos as evidence. In the office, Surveyors then use sophisticated software, such as Auto-cad to draft plans and map the onsite measurements. Surveyors work on a diverse variety of projects from land subdivision and mining exploration, to tunnel building and major construction, which means no two days are the same. They are experts in determining land size and measurement. They also give advice and provide information to guide the work of engineers, architects and developers.

According to Renishaw plc, laser scanning is not only used in land surveying but is being adopted in more and more industries, since it gives detailed, accurate data, very quickly, and with fewer manpower requirements, saving companies costs. Surveying is important and most of us depend on it so as to ensure order in the physical world around us.

Surveyors play an integral role in land development, from the planning and design of land subdivisions through to the final construction of roads, utilities and landscaping. Surveyors are the first people on any construction site, measuring and mapping the land. These primary measurements are then used by architects to understand and make the most of the unique landscape when designing and engineers to plan structures accurately and safely, ensuring buildings not only fit with the landscape but are able to be constructed.

According to Haglöf Sweden AB, It is valuable for everyone to keep track of assets to maintain control and healthy growth. Standardization, calibration and control systems are used in all industries, and when measuring, storing and processing data on-site, error sources are efficiently minimized. Problem areas are detected in time and actions are based on facts and figures.

It is necessary to mark the boundaries on the ground, so that they are clear to observers standing on or near the property. Also surveying and land surveying is intended to provide the evidence needed by the title insurer to delete certain standard exceptions to coverage and thereby provide “extended coverage” against off-record title matters including matters that would be revealed by an accurate survey.

Many properties have considerable problems in regard to improper bounding, miscalculations in past surveys, titles, easements, and wildlife crossings. Also many properties are created from multiple divisions of a larger piece over the course of years, and with every additional division the risk of miscalculation increases. The result can be abutting properties not coinciding with adjacent parcels, resulting in gaps and overlaps.

Many times a surveyor must solve a puzzle using pieces that do not exactly fit together. In these cases, the solution is based upon the surveyor’s research and interpretation, along with established procedures for resolving discrepancies. This essentially is a process of continual error correction and update, where official recordation documents countermand the previous and sometime erroneous survey documents recorded by older monuments and older survey methods.

GPS Surveying

The market for survey grade GNSS as well as for GIS handheld GPS is increasing in Africa. Survey grade GNSS is used by Land surveyors for new township layouts, and by construction
companies for survey control points and for staking out roads etc. It is needed for drone surveys for ground control points, and is increasingly used for precision agriculture.

According to Mr. Dave Beattie of Autobild Africa a distributor of a wide range of trusted surveying equipment from South Africa, some African countries already have CORS systems for getting accurate fixes from what is called NTrip Rovers, using cellphone networks to access the CORS bases via internet. Those that do not have such systems are looking to implement them soon.

“Because GNSS equipment is solid state electronics, and because accuracies of different makes is the same, there is very little to differentiate between makes of GNSS. Ease of Use, flexibility and Support are the most important things to look for. Most makes now offer Windows controllers with universally used software such as Field Genius or Carlson Surv Ce. These programs are well established, used around the world and have built-in co-ordinate systems for all countries. They also work with all makes and models of GNSS as well as total stations,” he says.

“If I were considering purchasing I would be wary of buying a system that uses controllers and software built by the GNSS brand. This is their way of tying in customers for life. To expand ones system to several GNSS units, ones options become severely limited,” he adds.
Mr. Beattie further mentions that, to replace these controllers is very expensive. With Windows controllers and universal software one has unlimited choices and flexibility. There are universal protocols used by all brands such as RTCM or CMR+. Some manufacturers program their GNSS antennas to communicate in Brand specific protocol. Once again, these brands should be avoided because it limits one to that brand only for future purchases and expanding ones system.

“For example you may have a base and rover set and need to expand by buying another rover. Keep your options open by sticking to windows systems as mentioned above. Then support is the next big issue, and of course price. Prices can vary significantly but, unlike Opto mechanical instruments, GNSS products are all generally robust, lightweight, and give the same accuracies,” he affirms.

Surveying Equipments and Level Set up

SURVEYING EQUIPMENT AND LEVEL SET-UP

The opposite figure shows a LEICA Level packages.

Make sure the surveying equipment you will borrow is reliable and in good working order.

To ensure this a two peck test must be carried out each 
time you borrow a level.

Surveying instruments that you need to complete your projects, 
can be borrowed from the following persons:

Equipment

For carrying out your project work you need to borrow the following equipment:

LevelTripodStaff (5 metre)
Staff bubbleMeasuring tape (50 metre)Wooden pegs (if needed)

Additional equipment is needed for some other projects and the lecturer will inform you what you need to do this exercises.

The following information is extracted from 'LEICA NA720 User Manual'.

Level types
There are different types (Leica, Sokkia, Wild) of levels you can borrow. The level opposite is a Leica NA720. Most level instruments have an automatic horizontal adjustment of the line of sight. Levels are supplied in a case in which the instrument can be shock proof stored. All survey levels operate in a similar way. The function and operation of levels is explained using the Leica 720 which is the most available instrument in the storerooms.
Endless drive (both sides)Bubble level (to check horizontal plane)Mirror to view bubble levelBase plate (sits on tripod)Footscrew (to adjust the horizontal plane)Eyepiece (focus adjustmentKnurled ring (for horizontal circle reading)ObjectiveCourse aiming deviseFocusing knob (turn until staff reading is clearly visible)Window for digital angle reading (see 7)

Setting up the tripod

Loosen screws of tripod legs, pull out to required length and tighten screws.In order to guarantee a firm foothold sufficiently press the tripod legs into the ground. When pressing the legs into the ground note that the force must be applied along the legs.Check all screws and bolts for correct fit.When setting up the tripod pay attention to a horizontal position of the tripod plate. Minor inclinations of the tripod can be corrected with the footscrews of the tribrach.Place level onto tripod head. Tighten central fixing screw of tripod.Turn footscrews A and B simultaneously in opposite directions until bubble is in the centre (on the imaginary "T").Turn the instrument 90° and then turn the foot screw C until bubble is centred.If you want to centre an instrument over a ground point:

  1. Attach plumb bob and arrange the tripod in such way that the plummet is over the point.
  2. For fine adjustment loosen central fixing screw slightly and shift instrument parallel on tripod until the plummet is exactly over the point.
  3. Tighten central fixing screw.

Focusing telescope

Aim telescope against a bright background (e.g. white paper).

Turn eyepiece until reticule is sharp-focused and deep black. Now the eyepiece is adapted to your eye.

Aim telescope on staff using the coarse aiming device.

Turn focusing knob until image of staff is sharply focused.

Levelling staffs (rods) and accessories

There are many types of staffs, with names that identify the form of the graduations and other characteristics. Staffs can be one piece, but most of them are sectional and adjust the length by telescoping..

The metric staff has major numbered graduations in meters and tenths of meters (there is a tiny decimal point between the numbers). Our staves have an ''E'' shape mark (or its mirror image) with horizontal spaces between them of 10 mm.

When viewed through an instrument's telescope, the observer can easily visually interpolate a 10 mm mark to a quarter of its height, giving a reading accuracy of 2.5 mm. On one side of the rod, the colours of the markings alternate between red and black with each meter of length.

The Black arrows indicates where to push to extend the staff to its full length.

                                                                

Staff readings

The figure below shows three different staff readings:

It is easy to read (b) and (c) because the cross-hair is exactly on a mark division. The reading for (a) is between 1.630 and 1.640. To assess the mm reading you have to estimate where the position of the cross-hair is. For (a) the reading is 1.636. The millimeter reading is to be estimated and can very between ± 1 mm.

reading (a) is 1.636 (b) is exactly 1.500     and (c) is 1.580

Spirit & line levels

There are a wide range of spirit levels to meet the varying requirements of specific jobs. The majority of those used on construction work are made of powder coated aluminum or die cast construction. The length varies from 800 mm to 2000 mm. Spirit levels are very handy for short distance levelling (depending on the spirit level up to 2 metres and with straight edge up to approximate 5 metres). The straight edge is used if the the points to be levelled exceed the length of the spirit level.

The line level has been designed and made with two small hooks to hold it on a line as shown in the figure above. A line level is a level designed to hang on a string line. The level must hung in the center of the string and each ''leg'' of the string line extends the levels plane.
The line level is a simple surveying instrument which can be used to lay out contours and gradients, and also to assist measuring horizontal distances at slope.

Plumb bobs

 A plumb-bob or a plummet is a weight with a pointed tip on the bottom that is suspended from a string and used as a vertical reference line. This instrument has been used since the time of the ancient Egyptians by bricklayers, masons, and carpenters to ensure that their constructions are "plumb", or perfectly upright. It may also be used in surveying to sight a point on the ground that is not readily visible. Small plumb bobs are often included in the kits of various instruments such as levels and theodolites. They are used to set the instrument exactly over a fixed datum marker, prior to taking fresh readings. In conjunction with the line-level the can also be used to assist the horizontal measurement on slopes.

Water level

An old device but a simple instrument for measuring the level differences of two points. This level, is illustrated in the opposite figure. The two levelling staffs are of the same length with a graduated tape attached to each stave. The tube is filled with water. The ends of the tube are fitted with rubber stoppers to prevent loss of water. The total length of tube defines the range of the instrument.

Straight edge

A 'straight edge' in conjunction with a spirit level and tape measure can be used to establish a gradient. The straight edge is usually 3 to 5 metres long and set horizontally with the aid of a spirit level. This method should be used for the measurement of gradients which continue only for short distances, e.g. to calculate the horizontal distance shown in plan-views. The figure below shows how a gradient for the ground profile is found.

Measurements along a slope

Distinguish between a horizontal distance and a slope distance. All distances should be measured 'horizontally'. Do not measure along slopes. Sag (tape are not supported for its length will sag under the influence of gravity) and to a lesser extent temperature may have an effect on the distance measurement also. To reduce the sag break tape measurement into shorter lengths.

The sum of horizontal lengths (L₁ & L₂) equals the horizontal distance of the slope from A to C. Remember the horizontal distance is always shorter than the measurement on the slope.

For an accurate measurement, the tape should be held horizontal and straight with a specified tension applied to it.

Slopes - Gradient calculations

A slope is the steepness, incline, gradient, or grade of a straight line, and it is defined as the ratio of the "rise" divided by the "run" between two points on a line. The gradient of a straight line shows how steep a straight line is. The slope of a line in the plane containing the y (rise) and x (run) axes may be represented as:

(a) gradient      (1:50;  1:2)
(b) percentage  ( 2%; 50%)(c) decimal fraction  (0.02;      0.5)
(d) angle                  (1.146°;  26.565°) 

Here are the calculation example of the figures shown in the "Straight edge" section

(a) Gradient     200 : 3000 = 1 : x     x = 15     Gradient = 1 :15

(b) Decimal fraction 200/3000 = 0.066666     Fraction = 0.0667

(c) Percentage multiply decimal fraction by 100
                     0.06666 × 100 = 0.06666            Percentage = 6.667%

(d) Angle in degree inverse tan-function rise over run (tan^-1 function on calculator)
         tan a = 200/3000 = 0.06666                     a = 3.814°

Distance measurement methods

For measuring a distance we use steel or fibre glass tapes as shown in the opposite figure. They are available in 30 metre and 50 metre length.

A more sophisticated method is to use the Electronic Distance Measuring (EDM).
We will not use this method. EDM devices use electromagnetic waves, infrared waves, or lasers to measure distances precisely.

Approximate (fairly accurate) distance measurement method is 'pacing' or using the 'stadia lines' on the reticle of the level
Pacing
Don't try to pace out one metre with every step. Walk casually over 50 or better 100 metre counting the number of steps. Work out the length of a casual step and use this instead. The longer the walking distance the more accurate is the step measurement.
Example
If it takes you 65 steps to walk 50 metres; then your step is 50/65 = 0.77 metre. If you would waked 39 steps, then the distance is 39 x 0.77 = 30 m.
Stadia lines
The stadia lines on the reticle can be used for simple distance measurement. The distances intercepted on the vertically-held rod between two stadia hairs seen in the eyepiece gives the distance. Just multiply the difference on the rod between the top and bottom stadia lines by 100* as shown in the figure below.

In the example above the distance between the top and bottom stadia hair is 62 mm. Therefore, the distance to the staff is 62 × 100 = 6200 mm or 6,2 metres.
* The 100 figure should be checked before beginning any survey by measuring the known distance with a tape.

Surveyors usually use total stations for land surveying. A total stations is a combination of an electronic theodolite (transit), and electronic distance measuring device (EDM).

Other accessories

Optical square

Range PoleOpticle Square and Range Poles are used in surveying course No W5939

Change Plate - a small flat metal plate with a raised point in the centre that is used to support the staff on the ground. The plate is firmly embedded into the ground to stop the staff from subsiding.
There are various types of staff bubbles available to assist in keeping the staff in an upright position.
You will need pegs or stakes and hammer for Project 4 (Grid points for RL's) All can be borrowed from the surveying department.