Offset calculation exercise
Calculate the area and perimeter of the Lot
A chain line (line & figures = red) is set up across an existing polygonal shaped lot running from Station A to Station B with given measurements along the chain line as well as the offsets (lines & figures = green) measurements to all other corner pegs of the lot.
From the given survey data find the area in square metre (three decimals) of the lot and the perimeter in mm (running metre of fencing).
As can be seen all single areas a to i consist of triangle and Trapeziums.
To calculate the area you only need to know the following formula:
(a) triangles and (b) trapeziums
All offset measurements are perpendicular to the chaine line
The area of Triangle a is 17.202 × 22.183/2 = 190.796 m²
Triangle b is 15.199 × 18.999/2 = 144.383 m²
The area of Trapezium c is (30.091 + 22.183)/2 × (32.350 - 17.202) = 395.923 m²
Trapezium d is (29.064 + 18.999)/2 × (38.410 - 15.199 = 557.795 m²
Finish the calculation for the rest of the areas (answer = 3,212 m²)
The calculation of the perimeter of the lot is more cumbersome. You may use either Pythagoras theorem or the tragicomic functions.
length of a1 = √ (17.202² + 22.183²) = 28.071 m
b1 = √ (15.199² + 18.999²) = 24.330 m
c1 = √ [(32.350 -17.202)² + (30.091 - 22.183)²] = 17.088 m
d1 = √ [(38.410 -115.199)² + (29.064 - 15.199)²] = 18.783 m
Finish the calculation for the rest of the boundary sites (answer = 210.707 m)
To use trigonometric function to calculate the perimeter is too cumbersome as no angles given.
Practical Project 2 (rectangular coordinates)
Setting out a perpendicular line using builders triangle 3, 4, & 5 instead with an optical square.
Practical Project 3 (polar coordinates)
The method of polar coordinates is used for Project 3. This project requires the theodolite, which must be booked in advance (only one is available).
Put a string line around all pegs to show the building outline.
In order to describe the position of a point, two coordinates are required. Polar coordinates need a line and an angle. Rectangular (Cartesian) coordinates need two points within an orthogonal system. The total station measures polar coordinates; these are recalculated as Cartesian coordinates within the given orthogonal system, either within the instrument itself or subsequently in the office.
Click here for a comparison of polar and rectangular coordinates.
Working with Range Poles
A range pole (also called a lining rod) is a metal or wood pole, usually about 2 metre long and about 20 mm in diameter; it is provided with a steel point or shoe and painted in alternate bands of red and white to increase its visibility. The range pole is held vertically on a point or plumbed over a point, so the point may be observed through an optical instrument. It is primarily used as a sighting rod for either linear or angular measurements.
Setting out straight lines over a short or long distance
A small hand instrument used in setting off a right angle. The optical square has two plane mirrors placed at an angle of 45° to each other. Two range poles are placed on a chain line at position A and B. Range pole A should be seen in the lower mirror, and the range pole B in the upper mirror. Move range pole C (middle slot) in left or right direction until its lined up with the range pole in the lower and upper mirror. The lines to the point of observation from the two observed objects will then meet in a right angle.
( In another form of optical square, a single plane mirror makes an angle of 45° with a sighting line. it used for sitting out a right angle.)
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