Survey
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Building Site Surveying and Set Out 2182K 1 Topics in module 1. Surveying laws and geometry 2. Survey plans, bearings and set out 3. Measuring equipment 4. Leveling devices, tools and instruments 5. Using your level and level books 6. Grid levels, areas and volumes 7. Plotting and calculating grades 2 Topic 1. Surveying laws and geometry Contents The laws relating to surveying Surveyors and survey qualifications Cadastral surveying Survey marks Geometry revisited The measurement of angles Right-angled triangles and Pythagoras’s theorem Triangles without a right angle Triangles and building sites Learning outcomes On completion of this section you will: • know the various Acts of parliament which affect building setting-out • know which areas of surveying require the services of a practicing Registered Surveyor • be able to identify various survey marks • be able to calculate missing values in a right-angled triangle and use trigonometrical ratios to calculate oblique triangles • be able to use these triangles as an aid in setting out buildings. Introduction Setting out for building construction requires some knowledge of basic surveying. Part of this section is devoted to a brief introduction to land surveying in Australia. Surveying has been described as the second-oldest profession. About 5000 years ago, surveyors were in great demand in Egypt to mark out the corners of each farm allotment following the annual flooding of the land by the River Nile. This was most important, because the Pharaohs based taxation on the area of land owned and the estimated yield from that area of land. In the Book of Genesis in the Bible, Moses exhorted the Israelites, ‘Thou shalt not remove thy neighbour’s corner mark’. Just 2000 years ago the 3 Roman agrimensor (agri- for land and mensor for measurer) was in great demand to set out villages, roads and aqueducts. In Australia, surveying is one of the very few professions which are controlled by government statute. There are laws for the qualifications of surveyors, laws as to the type of surveying which only surveyors can carry out, the type of marks which are placed and even the dimensions of these marks. The laws relating to surveying As mentioned in the introduction, there are several Acts of parliament or parliamentary statutes which affect the practice of land surveying in Australia. Each state has its own specific laws. Here are some of those laws which apply specifically to NSW. The principal Act of parliament which controls the practice of land surveying is the Surveyors Act, which sets out: • the academic qualifications required for registration as a surveyor • the types of surveys which only a Registered Surveyor can carry out • the types of survey marks which are used to define a parcel of land • the dimensions of these marks. Some other acts of parliament which have a bearing on surveying are the Local Government Act, the Real Property Act and the Survey Coordination Act. Surveyors and survey qualifications Within any surveying organisation there are three levels: • Registered Surveyor • Survey technician • Survey field hand. Of course these three levels are not clearly defined and there are ‘grey’ areas in between each level. There are also other support staff such as clerical workers, draftspeople and so on. 4 Table 1: Three levels of surveyors’ qualifications The Surveyors Act specifies that any firm or business setting up as land surveyors must have Registered Surveyors as its principals. Registered surveyors For registration as a surveyor by the Board of Surveyors, the candidate must have a degree in surveying from a recognised university. On completion of the degree, the candidate must then complete two years as an articled pupil to a Registered Surveyor. On completion of the two years, the candidate then must pass a practical and oral examination set by the Board of Surveyors. This final examination carries over five days. Each year in the Government Gazette, the Board of Surveyors publishes a list of all surveyors who are registered. Technician surveyors Technician surveyors are those who have completed a degree at the university and have not for various reasons bothered with registration, or have completed a surveying course through TAFE (Surveying Certificate or Surveying Diploma). There are some technicians without qualification, who through skill and expertise are competent to use surveying equipment and carry out the necessary calculations. Survey field hand The survey field hand is the equivalent of the surveyor’s labourer—the one who has to scramble over fences, is chased by savage guard dogs, confronts irate property owners and invariably has to cut a line through the thickest patch of blackberry bush within kilometres! 5 Cadastral surveying The term cadastral simply means boundary surveying. The Surveyors Act states that cadastral surveys must be carried out by a Registered Surveyor or by a survey technician under the immediate supervision of a Registered Surveyor. This part of the Act is very important because it means that only Registered Surveyors or technicians under immediate supervision can mark out the corners of a property or define the location of a boundary. The two types of boundary survey which are of concern to us are surveys for property identification and surveys to mark property boundaries. Surveys for property identification The boundaries of a property are located but not necessarily marked. The survey identifies that the land which is the subject of the survey agrees with the description of the land given on the title documents. Any improvements on the property are usually related to the property boundaries, and the survey report also shows any restrictions on the title by way of easements or covenants, and also any encroachments on the land or by the land on adjoining property. Surveys to mark property boundaries In this case the corners of the property are marked, and sometimes, depending on the length of the boundary or nature of the boundary, line marks are placed along the boundary. Additional line marks may also be placed at the request of the client as an aid to building setting-out. There are other types of surveys defined by the Act which are used for the definition of boundaries. These are surveys to create new titles or to amend existing property titles. An example is a subdivision survey where new allotments are created. It is important to note that cadastral or boundary surveys are the only surveys which are specified by the Surveyors Act requiring supervision by a Registered Surveyor. Survey marks Marking corners The Surveyors Act specifies the type of marks to be used for marking 6 corners, angles and line marks on property boundaries. For example in NSW, for an urban holding, the dimensions of the peg marking a corner should be 75 mm by 50 mm and 450 mm long. These pegs are driven into the ground leaving only 75 mm of the top of the peg above ground. The actual corner is marked on the top of the peg by a clout. Each state has its own standard for survey marks. Become familiar with the type of mark used m your state to ensure that you do not become confused when setting out a building and use the wrong marks. Where it is not possible to place a peg (for example, where the boundary is fenced), the corner is marked by a galvanised clout or by a spring-head roofing nail. In rock, the corner is marked by a drill-hole in the rock, with wings cut in the rock indicating the direction of the boundary lines. For rural allotments in NSW, the corners are marked by pegs 75 mm by 75 mm, with trenches or a line of stones two meters long on each side of the peg to indicate the direction of the boundaries. These are called Lock spits. The centre of the peg is taken as the actual corner. 7 Figure 1 shows some of the different types of marks used for marking property boundaries. Other survey marks There are many other marks specified by law which surveyors place when carrying out surveys for new subdivisions or for redefinition of a land title. Some of these are called permanent marks, reference marks and state survey marks. Reference marks can take the form of a drill and wing similar to the drill hole and wings which indicate a property corner. Take care if the mark appears to be ‘off-line’ to the rest of the boundary marks. There are also two pegs which are used to mark points which are not corners of properties. First there is the ‘dumpy’ peg. This is a short peg the head of which is much smaller than the property corner peg. Note that dumpy pegs are never used to mark property corners. These pegs are not described in the Surveyors Act. The uses to which these pegs 8 are used are to mark corners of buildings, centre lines of pipelines, centre lines of roads and driveways, and anything else not related to property boundaries. By the same token, survey pegs described by the Surveyors Act are never used for anything else but property corners. This is to avoid confusion about marks. Indicator pegs are used to indicate the location of a dumpy peg, because dumpy pegs are driven so that the top of the peg is flush with the ground. Indicator pegs are 50 mm by 20 mm and a length sufficient so that the top of the indicator will show above the paspalum or other grass which will hide the location of the dumpy. One final point before we leave survey marks: just as Moses could call down fire and brimstone on anyone who removed his neighbour’s corner mark, the Board of Surveyors has power under the provisions of the Surveyors Act to impose penalties on anyone who willfully removes or disturbs a survey mark. Not quite fire and brimstone, but a heavy fine, and the miscreant also has to pay for the replacement of the mark in its correct position. 9 Geometry revisited This is not going to be a detailed or heavy exposé on the proof of theorems with which you may have battled at school. We will look at some very basic formulae and the application of the formulae to solve right-angled triangles. Many surveying calculations are based on simple right-angled triangles. Before we delve into triangles, there is one area for which clarification is needed, the measurement of angles. The measurement of angles You may recall that a degree is divided into 60 minutes (‘) and each minute is divided into 60 seconds (”). One second is one three-thousandsix-hundredth of one degree (‘1/3600°). This may seem a very minuscule fraction, but surveyors are used to working down to fractions of this size. In fact, the Surveyors Act states that all angles shall be shown to the nearest five seconds. Converting degrees, minutes and seconds into decimals Unfortunately calculators cannot work directly in degrees, minutes and seconds. We need to convert these fractions of angles into decimals of a degree. Scientific calculators have a built-in function key which allows you to enter degrees, minutes and seconds, and this key will then convert them into decimals. Before you reach for your calculator to see how this function key works, here is the simple routine to convert angles to decimal degrees: minutes seconds Unfortunately all calculator manufacturers seem to have their own ideas how the angle-conversion function key should work. Refer to the handbook which came with your calculator to find out how your particular machine works. Whichever way your machine requires the entry of angles, remember you 10 must always convert angles from degrees, minutes and seconds to decimal degrees before carrying out any mathematical operation of the angles. S Small fractions of degrees We have already mentioned small fractions of degrees. These small fractions also carry over when you convert to decimals. For example, one minute = 0.0166667 in decimal degrees. One minute and 5 seconds = 0.0180556 decimal degrees. You can see that there is a substantial difference in the third decimal place. Your calculator will work to 7 or 8 places so always show all these places. Do not round off to four places. You will introduce errors. One final point when working with angles, always show high-order zeros for minutes and seconds. That is 5 minutes is always shown as 05’ and not 5’.3 minutes and 5 seconds is shown as 03’OS”. This is to avoid the possibility of errors. 11 Check your progress 1 Work through these problems. Convert the following angles to decimal degrees: show your answers to seven decimal places. 1. 15°08’30” _____________________________ 2. 63°27’55” _____________________________ 3. 41°03’45” ___________________________ 4. 88°57’05” _____________________________ 5. 3°O1’50” _____________________________ 6. 19°33’lO” ___________________________ 7. 71°O8’25” _____________________________ 8. 57°46’SO” _____________________________ 9. 31°12’20” ___________________________ 10. 29°55’05” _____________________________ Right-angled triangles and Pythagoras’s theorem Pythagoras’s theorem Pythagoras’s theorem states that the square on the hypotenuse of a rightangled triangle is equal to the sum of the squares on the other two sides. Useful formulae Let’s have a look at a right-angled triangle and break this sentence down into simple, easy-to-remember formulae. 12 The hypotenuse of any triangle is the longest side. Now let’s try an example. Figure 4: A right-angled triangle In this triangle we are given two sides and require to determine the length of the third side. 13 a2 =b2+c2 =42 32 = 16 + 9 =25 a=√25=5 This is the classic 3:4:5 triangle and as you can see, the calculations are quite simple. Remember, if you are given the hypotenuse (the longest side) and one other side, the rule is to subtract and not add. Check your progress 2 Figure 5 shows six different right-angled triangles each with the value of one side missing. In each case calculate the missing value. 14 Figure 5: Right-angled triangles with missing values Sine, cosine and tangent Unfortunately the calculation of a missing side from two other sides is only part of the story. As you may have gathered from the previous pages, angles play an important part in the solution of triangles for missing values. There are three trigonometrical ratios related to right-angled triangles 15 which have an important bearing on our calculations. These are the sine, cosine and tangent ratios for angles. Defining sine, cosine and tangent These three ratios are: • The sine of an angle equals the opposite side divided by (over) the hypotenuse. • The cosine of an angle equals the adjacent side divided by (over) the hypotenuse. • The tangent of an angle is equal to the opposite side divided by (over) the adjacent side. A simple method to remember the ratios Note the initials/each line S = 0/H, C = A/H and T = 0/A, the three ratios. Figure 6 illustrates the opposite and adjacent sides to angles in a rightangled triangle. Figure 6: The sides of a right-angled triangle 16 Using the ratios How are these ratios used? In any right-angled triangle, if we are given the value of one side and either of the two angles (note that the right angle is always known), we can calculate all the other values in the triangle. Let’s look at an example. Figure 7: Right-angled triangle with missing information In Figure 7 we are given an angle and only one side. From this information we can calculate the other angle and the two missing sides. The given information in this triangle is one angle and the side opposite this angle. Given the opposite side, then the appropriate ratio to use is the sine ratio. sin = opposite ÷ hypotenuse The equation needs to be rearranged to give the two known values on one side. Hypotenuse = opposite ÷ sin H=28.679÷sin35° = 28.679 ÷ 0.5735764 =50 Adjacent side = opposite ÷ tangent A=28.679 ÷ tan35° 17 = 28.679 ÷ 0.7002075 = 40.958 The adjacent side could also have been calculated from the hypotenuse which has just been determined. adjacent side = hypotenuse x cos A = 50 x cos 350 =50x0.8191520 = 40.958 As you may recall from school days, the sum of all the angles in any triangle must add up to 180°. In a right-angled triangle the right angle is 90°, so the other two angles must add up to 90°. angle=90—35 = 55° Now we have determined all the values off the triangle. Are you sure they are correct? There is one final calculation which must be carried out. Check your work! √(28.6792 + 40.9582) = √12500 =50 This last step, checking your work, is most important. Do not neglect it. There is nothing more disconcerting than watching the ready-mix concrete truck drive away having delivered its load, and then discovering that you have made an error in setting out caused by an incorrect calculation. Checking calculations When checking calculations, it is not enough simply to repeat the calculation. If you have made a mistake, then there is every likely hood that you will make the same mistake again. If possible, always check calculations by using a different method. In the above calculation, notice that I have used a different method to calculate the length of the hypotenuse as a check. 18 In the initial calculation, the hypotenuse was calculated using the sine function. After calculating the third side, the hypotenuse was recalculated using Pythagoras. This checked not only the original calculation of the hypotenuse, but also the calculation of the third side. Surveyors claim to never make mistakes! Of course, this is not true. Everyone makes mistakes and surveyors try to find their mistakes before anyone else finds them! Most survey work is either self-checking, or the work is done using two different methods. We will come across selfchecking routines later in this module. 19 Check your progress 3 Figure 8 shows four right-angled triangles, each with an angle and one side given. Calculate the missing values for each triangle. Triangles without a right angle What you need to know Right-angled triangles are a unique form of triangle. In general, most triangles are oblique triangles. That is, the three angles are all different and not one of them is a right angle. The methods for calculating oblique triangles are much more complex than for right-angled triangles and are beyond the scope of this module. 20 We will come across oblique triangles a little later in another section of this module, but even in there you will not be called upon to determine missing values or even calculate with any accuracy. For nearly all your surveying calculations you will be required to deal with only right-angled triangles. Two important rules Just before we leave the theoretical side of triangle calculation, there are two points you should always keep in mind. These two points apply to any triangle whether right-angled or oblique. • The hypotenuse is always shorter that the sum of the other two sides. • The length of any side is always of the same magnitude of the opposite angle. The second rule may need a little explanation. The hypotenuse being the largest side is always opposite the largest angle. In a right-angled triangle, the right angle is the largest angle and the hypotenuse is always opposite the right angle. The shortest side is always opposite the smallest angle. Triangles and building sites We will now apply the theory of right angle triangles from the previous pages to building sites. Town planners delight in creating building allotments where the shape of the allotment is not square. The first problem is will the building as designed fit on the block of land? Never assume that the frontage of a block of land is the actual width of the block. When we refer to the width of a block of land, width means the square width, the width at right angles to the side boundary. Defining square width Figure 9 illustrates what is meant by the square width. Looking at the diagram, it is obvious the length of the frontage will be greater than the width. 21 Calculating square width Now refer to Figure 10, the same parcel of land but with some dimensions, the angle formed by the side boundary with the frontage and the length of the frontage. What is required is the square width of the lot. Figure 10: Allotment frontage with dimensions The first step in this calculation (or any calculation involving angles) is to convert the angle to decimal degrees as shown earlier in this section. 80°47’15” = 80.7875 square width = 15.44 x sin (80.7875) = 15.24 meters. Taking this type of calculation one step further, you have been given a plan of a building which the owner wants erected on his land. Figure 11 illustrates this situation. Given that the Local Government Act requires a 22 minimum distance from wall to boundary on each side of the dwelling of 900 mm, will the building comply? Figure 11: Allotment with proposed dwelling The total width of the building is: 3500 + 5000 + 5300 = 13800 mm or 13.8 meters 71°14’ = 71.233333 square width = 16.1 x sin (71.233333) = 15.244 available excess = 15.244 — 13.8 = 1.444 meters the building will not comply with council requirements as 1.8 meters is required. Check your progress 4 Figure 12 shows a plan of land? What is the square width of the land? 23 Figure 12: Land with irregular frontage Assignment: Unit 1 Marks 1. The NSW Surveyors Act states that cadastral surveys shall be carried out by a Registered Surveyor. Cadastral surveys include the marking of property boundaries by pegs or other authorised means. If you were to set up a theodolite on an existing corner peg for the purpose of setting out a dwelling on the land, would you be infringing the requirements of the Surveyors Act? Answer simply yes or no, stating briefly your reasons for your answer. 2. You have been given a plan of a proposed dwelling on a parcel of land. Given that the Local Government Act provides for a minimum wall to boundary distance of 900 mm and the eave overhang to boundary 24 distance of 675 mm, will the building comply with these requirements? The position of the building and the pertinent lot dimensions are shown on Figure 1 (next page). 3. Figure 2 shows a driveway onto a property. The driveway is 3 m wide and is to be paved with concrete for the full width. From the information given, calculate the distance apart the gateposts must be on the frontage to clear the concrete. 25 Figure 2: Plan showing location of driveway 4. Figure 3 shows the frontage and side boundaries of an irregular shaped parcel of land. The local council has fixed a building line of 6 meters on the land. Determine the distance from the front corner to the position of the two pegs marking the building line. If the frontage of the dwelling is to be square off the northern side boundary and the wall to boundary distances to be 1 metre, what is the available width for the building? (The distance to be determined is shown on the plan.) 26 27