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E4004 Surveying Computations A. Area Problems. To Cut Off an Area by a Line Passing Through a Fixed Point. The bearing and distance BP is known. The bearing BX is known. The required area BPX is known. Calculate the bearing and distance PX and the distance BX. P. Brg Dist. B. Brg. X.
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E4004 Surveying Computations A Area Problems
To Cut Off an Area by a Line Passing Through a Fixed Point • The bearing and distance BP is known • The bearing BX is known • The required area BPX is known • Calculate the bearing and distance PX and the distance BX P Brg Dist B Brg X
To Cut Off an Area by a Line Passing Through a Fixed Point • The angle at B is determined from the bearing difference • The general formula for the area of a triangle is P B a Brg Dist B C b Brg X A
To Cut Off an Area by a Line Passing Through a Fixed Point • The bearing & distance of the line PX can be calculated by closing PBX • Also check that the area PBX calculates to the correct area by using the CLOSE program P Brg Dist B Brg X
To Cut Off an Area by a Line Passing Through a Particular Point • A farmer wants to fence off a particular area from a large paddock.There is an existing trough which must be accessible to stock on both sides of the new fence.
To Cut Off an Area by a Line Passing Through a Particular Point • The bearings of BC and BD are known. • The bearing and distance BP can be measured. • The required area is DA C Brg P Brg Dist B Brg D
To Cut Off an Area by a Line Passing Through a Particular Point • Note that there will be two solutions • Such that C’ C Brg P Brg Dist B Brg D’ D
To Cut Off an Area by a Line Passing Through a Particular Point • Let C x Brg P Brg a Dist b B y Brg D
To Cut Off an Area by a Line Passing Through a Particular Point C x Brg P Brg a Dist b B y Brg D
To Cut Off an Area by a Line Passing Through a Particular Point Multiply both sides of the equation by, x sin(a+b) Re-write in terms of x C x Brg P Brg a Dist b B y Brg D
To Cut Off an Area by a Line Passing Through a Particular Point Make the LHS equal zero This equation is in quadratic form and can be solved for x C x Brg P Brg a Dist b B y Brg D
To Cut Off an Area by a Line Passing Through a Particular Point • Write a program to solve for x in a quadratic given values for a, b and c • OR write a solver program which will solve for x, a, b or c
To Cut Off an Area by a Line Passing Through a Particular Point When the Figure is not a Triangle • It is required to cut off a given area CQRSTD by a line passing through P • The bearings and distances QR, RS and ST are known whilst the position of P has been located from Q C • Only the bearings are known for CQ and TD Brg Q Brg & Dist R P Brg & Dist DA S T Brg D
To Cut Off an Area by a Line Passing Through a Particular Point When the Figure is not a Triangle • Extend CQ and DT to intersect at B • The figure CBDF is the same as that formed in the earlier example provided the required area is made equal to the sum of Area QRSTB and DA • The dimensions of lines TB and BQ can be calculated by closing QRSTB and the line BP by closing BQP C Brg Q Brg & Dist B R P Brg & Dist DA S T Brg D