Route Survey Of The Stretch Of Road From Oriawo Along Ogbomoso Road, Oyo To School Of Science, Sabo Oyo Town, Atiba Local Government Area, Oyo State

4.2.1 FORWARD COMPUTATION
4.2.1.1 BEARING REDUCTION
This is the part of the exercise in traverse forward computation where the angular accuracy could be determined whether the traverse is within allowable error. The following formulae were used for the bearing reduction.
(i)    Back bearing = forward ± 180°
(ii)    Forward bearing = back bearing + observed angle.
4.2.1.2 CORRECTION TO BEARING
Note: - correction may be positive (+) or negative (-)
The above formulae were used for the reduction of bearing in this project. The reduction started from initial bearing between FSS2/GPS/121 and FSS2/GPS/120 and closed on the bearing of the line FSS2/GPS/03 to FSS2/GPS/04.
4.2.1.3 COORDINATES REDUCTION
The corrected bearings and true horizontal distances (length) measured were used to compute for latitude (∆N) and departure (∆E) of all traverse stations with the use of the following formula:
∆N = L COS Ø
∆E = L SIN Ø
Where Ø is corrected bearing
 L is corrected distance
Therefore, to get the provisional coordinate of a new station, i.e. northing and easting, for example, to get the coordinate of NL1, thus as the coordinate of FSS2/GPS/11 are known and the coordinate differences of the line from FSS2/GPS/11 to NL1 are also known then the coordinates of NL1 are simply obtained:
Easting  of NL1=Easting of FSS2/GPS/121 + ∆E (difference in eastings)
Northing of NL1=Northing of FSS2/GPS/11 + ∆N (difference in northings)
See appendix 1 pg.1&2 for more deductions.
4.2.1.4 COORDINATES ADJUSTMENTS
The latitude and departure obtained in 4.2.1.3 were added successfully to the coordinate of FSS2/GPS/11 in order to determine the provisional coordinates of newly traversed stations to the last station which was FSS2/GPS/16 (closing control). At the end of the computations, there were misclosures in Northings and Eastings coordinate i.e. the last coordinates calculated was not equal to the coordinate of the station that the traverse closed on. These called for corrections, transit coordinate correction method was used to correct the provisional coordinates so as to get the final coordinates as stated below:
For Northing coordinate=Arithmetic sum of each station × miscl. in northings / Total arithmetic sum
For Easting coordinate =    Arithmetic sum of each station ×miscl. in easting / TotalArithmetic sum
Therefore, the provisional coordinate plus (+)coordinates correction is equals to corrected coordinates of the new stations. Corrected coordinates are written with red pen.
4.2.2    BACK COMPUTATION
This is the reverse computation process of the forward computation. The final coordinates gotten from forward computation were used. The difference between both Northings and Eastings coordinates were used to obtain corrected bearing and distance of each traverse station by using the following formulae:
∆N = NC2 – NC1
∆E = EC2 – EC1
Distance =     √ (∆N) ² + (∆N) ²
Bearing (Ø) = Tan-1 ∆E/∆N
Where ∆E is changes in easting coordinates
∆N is changes in northing coordinates
NC2 is Northing coordinate for station 2
NC1 is Northing coordinate for station 1
EC2 is Easting coordinate for station 2
EC1 is Easting coordinate for station 1
The line of the latitude and departure of each determine the quadrant and the actual bearing of the line i.e.
If ∆N is + and ∆E is +, then the bearing is Ø
If ∆N is - and ∆E is +, then the bearing is =180°-Ø
If ∆N is - and ∆E is -, then the bearing is =180°+Ø
If ∆N is + and ∆E is -, then the bearing is =360°-Ø