E4004 Surveying Computations A

1. E4004 Surveying Computations A Area Problems

2. 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

3. 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

4. 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

5. 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.

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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