LINEAR MEASUREMENTS PDF

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Module 2 LINEAR MEASUREMENTS Learning Outcomes On the completion of this module you should be able to:     

Describe the methods of direct measurement. Describe the uses of chains, tapes and bands. Describe the measuring of sloping distances using chains, tape and band by:  Stepping: using a clinometer Demonstrate the calculation of slope correction for distances measured on an incline. Demonstrate the graphical method used to correct distances measured on an incline.

2.0

Introduction In this module, you will learn the method of linear measurement using chains, tapes and bands. You will also learn how to carry out linear measurements when a building, trees, ponds etc. obstructs visions or in the way of measurements. The modules also covers slope correction.

2.1

Chain surveying Chain surveying is the type of surveying in which only linear measurements are taken in the field. This type of surveying is done for surveys of small extent to describe the boundaries of plot of land to locate the existing features on them.

2.1.1 Linear Measurement The linear measurement is the distance between the two given points or objects. The height of the object is the distance between the top and the bottom. Thus, we can define length as: “Total gap measured between the leftmost and rightmost end of an object in the mentioned system of.” 2.1.2 Methods of Linear Measurements Various methods are used for linear measurements may be grouped as:  Using chains, tapes and bands  By optical means and  Using electromagnetics distance measurements. In this study, our concentration will be on the use of chains, tapes and bands.

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2.1.3 Measurement with Chains or tapes Measurement of distances using chain or tape is termed as chaining. This is the accurate and commonly employed method is surveying. These instruments can be classified as chain, tapes and steel band.

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Chains Chains are the measuring instrument used in surveying formed by the 100 links of 4mm galvanized mild steel wire. These links are joined by 3 circular or oval wire rings. These rings provide the flexibility to the chains. When using a chain, the number of links between the two pegs is counted. The total distance is equal to the number of links multiplied by the length of one link (20 cm). Distance = number of links x length of one link EXAMPLE: Calculate the distance when given that 30 links have been counted and the length of one link = 0.2 m. ANSWER: Distance = number of links x length of one link = 30 x 0.2 = 6 m

Figure 2.1 Chains

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Figure 2.1.1

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Parts of Chains used in Surveying The chain consists of many small parts used for handling or reading the measurements.  At the ends chain is provided with brass handle with swivel joint so that it can be easy to roll or unroll the chain without twisting and knots.  At every 10th link is provided with a tally of one teeth, 20th link with a tally of two teeth and so on till 40th link. This is provided for the easy reading of measurements.  At the center of the chain is provided with a circular talley used for easy reading.

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

Types of Chains used in Surveying

Depending upon the length of the chain, these are divide into following types, 1. 2. 3. 4. 5.

Metric chains Steel band or Band chain Gunter’s chain or surveyor’s chain Engineer’s chain Revenue chain  o

Advantages and Disadvantages of Chains in Surveying Advantages of Chains in Surveying 

Chain survey is simplest and commonest method used in surveying exercises

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The equipment used to conduct chain survey are simple to use,

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The equipment used in chain survey can easily be replaced. For example, measuring rods can be replaced with measuring tape.

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This method does not involve complicated mathematical calculation.

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In chain survey few people are needed to conduct the survey. Normally chain survey team has three people Booker, leader and follower.

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Disadvantages of Chains in Surveying

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Simple chain survey cannot be conducted in built up areas and large areas.

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Simple chain survey is subject to several chances of errors of accumulation which may cause by problem of chain. The chain linkage may fail to stretch up properly and result in inaccurate data. Also clogging of chain may read to error in reading.

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It is time consuming

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It may not be conducted in areas with steep slopes or water logged areas. Chain survey is usually conducted in dry areas with gentle slopes. It becomes more complicated when survey is conducted in areas that are too wet.

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Chain survey becomes more complicated method when there are raised points (obstacles) in between areas to be surveyed

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Steel band or Band chain

These types of chain consist of a long narrow strip of steel of uniform width of 12 to 16 mm and thickness of 0.3 to 0.6 mm. This chain is divides by brass studs at every 20cm or instead of brass studs, band chain may have graduated engraving as centimeter. For easy use and workability band chains are wound on steel crosses or metal reels from which they can be easily unrolled. These steel bands are available in 20m and 30m length and the width of about 12-16mm. Surveyor's steel measuring tape, known as a 'standard band' or 'steel band chain.'

Figure 2.2

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Surveyor`s Steel Bands

Tape Measure

A tape measure or measuring tape is a flexible ruler used to measure distance. It consists of a ribbon of cloth, plastic, fibre glass, or metal strip with linear-measurement markings. Surveyors use tape measures in lengths of over 100 m. 2.2

Types of tapes

Tapes used in surveying are of three main types:

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2.2.1 Cloth or linen tape Cloth tapes are made up of closely woven linen, 12 to 16 mm wide. These tapes are varnished on outer surface so as to resist moisture. Cloth tapes are light and flexible. Cloth tapes are used for taking rough measurements such as offsets. Cloth tapes are available in lengths of 10, 20, 25, and 30 metres. The tape is graduated into metres, tenths and hundredth of a metres (Some to ½ cm) The tape is provided with a brass ring whose length is included in the total length of the tape. Cloth tapes are not used for accurate measurements because:

1)

Length of cloth tape is gets altered by stretching.

2)

Cloth tape is easy to twist and tangle.

3)

Cloth tapes are not so strong.

Figure 2.3 Cloth or linen tape 2.2.2 Metallic tapes A metallic tape is made of varnished strip of water proof linen interwoven with small brass, copper or bronze wires. Due to this tape does not stretch easily as a cloth tape. Metallic tapes are light in weight and flexible and are not easily broken. Metallic tapes are particularly useful in cross-sectioning and in some methods of topographical surveys where small errors in length of the tape are not given importance. Metallic tapes are manufactured in lengths of 2, 5, 10, 20, 30 and 50 metres. Tapes of lengths 10, 20, 30 & 50 metre are provided with a metal ring at outer end. Metallic tapes are supplied in a metal or leather case fitted with a winding device.

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Figure 2.4 Metallic tape 2.2.3 Steel tape A steel tape consists of a light strip of width 6 to 10 mm and is more accurately graduated as compared to cloth and metal tape. Steel tapes are available in lengths of 1, 2, 10, 20, 30 and 50 metres. The tapes of lengths 10, 20, 30 & 50 and 100 metres are provided with a brass ring at outer end, fastened to it by a metal strip of the same width of the tape. The length of the tape is included in metal ring. Steel tapes vary in quality and in accuracy of graduation, but even a poor steel tape is generally more useful and accurate as compared to cloth or metallic tape. Steel tapes are wound on a corrosion resisting metal case with winding device. Steel tape is a delicate and light weight instrument hence it cannot withstand rough usage. Tape should be cleaned, dried and oiled after use so that it does not get rusted.

Figure 2.5 Steel tape

Figure 2.6 Steel tape

Steel tapes are correct at standard tension (pull) of 6-10 kilograms force and at a temperature between 16oC to 21oC, these figures usually being specified for each tape. Note: 1 kg force = +/-9.81 Newton`s (symbol N). Newton scales are not available yet.

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2.3

Maintenance and handling of steel tapes Steel are brittle and elastic. Being brittle they easily break if not handled properly, and the following should be observed when using steel tapes:  Draw the tape out in straight line in the direction in which it is coiled.  Ensure that there are no kinks or lops in the tape when using it.  Do not allow vehicles to run over the tape, and avoid stepping on it.  The standard pull (6-10 kg f) should not be exceeded.  Steel tapes re liable to rust. Before putting a tape away after use, wipe it dry then wipe it with an oily rag.

2.4

Standardisation of steel tapes With constant, regular use, a tape will stretch or distort. Therefore, when you are about to take some measurements, the tape should first be compared against a standard tape. The standard tape is simply a tape which is only used for standardisation of other tapes. It thus receives no heavy usage, and should not have deformed. Because of the purpose for which the tapes are used they must be accurate, and if the tape is not correct the error must be known so that due allowance can be made. An error in the tape can be revealed by comparing the tape with legally accepted standard lengths in South Africa. These are found in certain government building in Johannesburg, Bloemfontein, Pietermaritzburg and Cape Town.

2.4.1 Standardising the tape A number of metal blocks are let into the floor of a long passage-way each with fine marks on it; they are placed so that the required distance (e.g. 0-100 m, etc.) are set out. The temperature at which the tapes must confirm with the established distance is indicated on each block is protected by a brass cover which is unscrewed and removed when tapes are to be standardised.

2.5

Miscellaneous notes on tapes

1. A ranging rod (or range rod) is a surveying instrument used for marking the position of stations, and for sightings of those stations, as well as for ranging straight lines. This are also used in conjunction with tapes in surveying. Ranging poles are straight round stalks, 3 to 4 cm thick and about 2 m long. They are made of wood or metal. Ranging poles can also be home made from strong straight bamboo or tree branches.

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Figure 2.7 Ranging rod

Ranging poles are usually painted with alternate red-white or black-white bands. If possible, wooden ranging poles are reinforced at the bottom end by metal points 2. Spring balance for use with tapes, this is a tension handle with a spring balance graduated to a pull of 10kg f. It is used to ensure that the correct tension is-obtained in measuring.

Figure 2.8 Spring balance

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3. Steep wind-up measuring tapes. This type of steel is used for measuring the depths of shallow boreholes (e.g. water borehole on farms). It is obtainable in length up to 60m, and is obviously limited to boreholes up to this depth only.

Figure 2.9 Spring balance

4. Flexible spring steel rule. This is a flexible type of short steel rule which, when drawn out from its case, becomes rigid and remains stiffly extended due to the slightly concave shape it is forced to assume. Upon release it springs back or easily pushed into its case. Available in 2,3 and 5m lengths.

Figure 2.10 “Metallic” woven measuring tape

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2.6      

Step chaining An alternative method of obtaining horizontal measurements without using angle measuring instruments is that known as step taping. This is a field method where the horizontal distances are obtained directly. The tape must be held horizontally and considerable tension is required to straighten the tape and avoid sagging. A plumb bob or plumbed ranging rod may be used to transfer the horizontal distance to the ground. The length of steps that can be adopted is limited by the gradient. At no time should the tape be above eye level, because plumbing becomes very difficult. As the gradient increases the length of step must therefore decrease.

Figure 2.11 Step chaining

Distance of Station 1 to Station 2 = D1 + D2 + D3 Step chaining can also be performed when measuring uphill. In this case, the rear person has to hold the end of the tape above the mark left by the front person, by using a plumb bob.

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Clinometer A clinometer is a tool that is used to measure the angle of elevation, or angle from the ground, in a right - angled triangle. You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, flag poles, buildings, trees (figure 2.12)

Figure 2.12 A fairly common use of a clinometer is to measure the height of trees, which is easily done. A point should be marked with a stake as far from the centre of the trunk of the tree as its estimated height, so that the elevation angle is about 45°, which gives the best "geometry." This distance D is measured with a tape. The observer then stands over the stake and sights the top of the tree, finding its elevation angle θ. The height H of the tree is then H = D tan θ + HI, where HI, the height of instrument, is the height of the observer's eye. All this is illustrated in the diagram.

A useful accessory is a levelling rod, which can be home-made at little expense. Since the clinometer has no powerful telescope, the reading of the rod must be evident from a distance if you use it as a self-reading rod. Alternatively, if you have a rod person, she can stand by the rod and move a finger or other marker up and down in response to your signals, then measure the distance with a tape. A self-reading rod can be made from a 1" x 4" x 10' choice pine board available at Home Depot. A bold pattern that can be estimated to a few centimetres can then be applied by stencil and matte black spray paint. Two examples are shown at the right. Colors can also be used to make distinctions.

With the levelling rod, the HI can easily be obtained. Set the index at 0°, and the clinometer becomes a level. Sight the rod from close by, and read the HI. This can, of course, be done by simply making a mark on a wall just in front of your eyes, and then measuring its height.

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2.7

Slope correction for distances measured on an incline

Distances measured on an inclination (slope) have to be reduced to the horizontal except in a certain case such as in some mine measuring where the plotting of results is done on the same plane as that on which measurements were taken. When you take a measurement with a tape along an inclined plane (along the natural slope of the ground), obviously, the taped distance is greater than the horizontal distance. This taped distance is represented by s. The difference between the slope distance and the horizontal distance (s – d) is called the slope correction. This correction is always subtracted from the slope distance. To calculate the slope correction, you should know either the vertical angle, A, or the distance in elevation h between the taped stations.

Formulae to reduce inclined distances to the horizontal (figure 2.13) 1. In a case where the vertical distance is known: Horizontal distance = inclined distance x cosine of vertical angle 2. In a case where the difference in elevation (h) is known:

√

2 2 a). Horizontal distance = (Slopedistance ) −( diff .∈elevation ) . b). Horizontal distance = slope distance- correction for slope

where correction for slope (Ch) =

diff .∈elevation ¿ ¿2 2 x slope distance

The correction is accurate only when the difference in elevation is small, i.e. so as to give a vertical angle to 8o 3. When the vertical angle is used, the formula for slope correction is shown as follows: Ch = s Versine A. Since: Versine = (1-cos A) then Ch = s (1-cos A) Where: Ch = the slope distance correction s = the taped slope distance (usually length) A= the vertical angle.

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Figure 2.13 Correction for slope distance.

Example 1 A distance of 100,000 metres was set off at a vertical angle 6 o. The difference in elevation between the two ends of line was known to be 10,450. Determine the horizontal line distance between the two points working to two decimals. Solutions Using formula 1 Horizontal distance = inclined distance x cos vertical angle = 100 cos 6o = 100 x 0,99452 = 99,452 = 99,45 m Using formula 2

slope (Ch) =

diff .∈elevation ¿ ¿2 2 x slope distance

=10,452 2 x 100

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Therefore horizontal distance = inclined (slope) distance - correction = 100,00 - 0.55 = 99,45 m

√ (Slopedistance )2−( diff .∈elevation )2

Horizontal distance = =

√ 100−( 10,45)2

=

√ 9890,80

)

= 99,45 m Using formula 3 Ch = s Versine A. = 100 versine 6o

Versine = (1-cos A)

= 100 x 0,00548 = 0,55 Horizontal distance = 100 -0,55 =99.45 m

Example 2 A line K-N was measured in three sections K-N 90,288 m at a slope of 3o44’20” L-M 72,408 m at a slope of 4o32’59” M-N 47,652 m at a slope of 2o09’07” Find the horizontal distance K to N

solution K-L = 90,288 m cos 3o44’20” = 90,096 m L-M = 72,408 m cos 4o32’59” = 72,175 m M-N = 47,652 m cos 2o09’07” = 47,618 m

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).

K-N = 90,096 m + 72,175 m + 47,618 m = 209,889 m

References:

1. 2. 3. 4. 5.

https://www.slideshare.net/RamprasadKumawat1/linear-measurement-130865063 https://civilseek.com/surveying-tapes/ http://www.vermessungsseiten.de/englisch/vermtech/guide/stand.htm https://www.slideshare.net/zewduminwuyedessie/surveying-chtwo http://engineeringtraining.tpub.com/14069/css/Correcting-For-Slope-422.htm

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