GET OBSERVED ANGLE AND BEARING USING TAPE MEASUREMENTS

The fundamental principal of the science and art of surveying are based on very simple geometrical concept. This concept generally stated that if two points in the field are selected and established (coordinated) and the distance between them measured (base line). These can be represented on paper by two points placed in a convenient position on the sheet and at a distance apart depending upon the scale to which it is proposed to plot the survey. Fig 1. A B 542855.214mE 542853.701mE 122293.904mN 122273.564mN From these initial points other points can be located by two suitable measurement in the field and plotted in their relative position, that’s the “ whole to part principle”. Let us examine possible methods of locating a point say point C with respect to the two given points A and B . Distance AC and AB are measured respectively. Point C is plotted on the base map by using a pair of compasses, as the intersection point of arcs with centers A and B and radii scaling the measured distances. In this way, the three sides of the triangle are known and in turn all the elements of the triangle can be measured, derived or computed. This system is employed in chain surveying method and trilateration. Also the triangulation method of surveying is based on this principle. Having four (4) points ABCD with points A and B coordinated and as a base line, with their distances B to C , C to D and D to A all known , as gotten with a tape. We can compute and derive the observed angle (OA) which in turn gives us the bearing from B to C, C to D and from D to A respectively. We compute and derive the observed angle (OA) by simple getting the distance of any of the diagonal, either from A to C or B to A, in turn we have a triangle with the distance or length of each sides known. A B Using the coordinates of A and B we derive its bearing and distance which is gotten using this simple formula: EB - EA = ΔE NB - NA = ΔN Where : EB = Easting of point B EA= Easting of point A NB = Northing of point B NA = Northing of point A Bearing AB = Tan-1 ΔE ΔN Distance L = √∆E^2+∆N^2 Now to compute for observed angle (OA) we figure out a triangle says ABD : where all the sides are known . Using the cosine formula : a2 = b2 + c2 – 2bcCosA Or CosA = b2 + c2 – a2 2bc We compute and derive angle A. using the same formula we compute for angle B , having computed for two angles we can now use the sine rule , to compute for the remaining angle. Sine formula : a = b sinA sinB or we simply use the triangle rule of sum of angles in a triangle is equals 1800 we also do the same for triangle BCD and compute and derive its angles (OA). We now make use of those angles and the first initial bearing derived using the coordinate to compute for the bearing of the other sides, using this simple formula; BB + OA = FB Where BB = back bearing which is ±180° for the initial bearing OA = observed angle ( computed angle) FB = foreward bearing .