1. Coordinate systems O.S. Grid Site Grid Norths Whole Circle Bearings
Partials
Polar Conversions
Radial Setting Out

2. Ordnance Survey Grid
Greenwich origin for O.S. grid ( =0 Meridian) but causes –ve grid values, hence:
Longtitude parallel to 2 West Meridian &
Origin Shifted west and south to allow only positive grid values in UK
Ref. By two letters and six figures for 100m accuracy (e.g. TH645589)
More accuracy not used with general OS maps
Eastings and Northings values for Surveying involve 5 integers and 3 decimals these are then in metres. ( e.g mE, mN)

3. Grid size and accuracy 60 65 50 55 Km 640 650 540 550 100m grid
643, 542
to a 100m corner square
6455,5443 to nearest 10m
1km or 1000m grid
1000m = 1Km, 100m = 0.1km, 10m = 0.01km, 1m = 0.001km
mE, mN

4. OS Grid to Site Grid conversions
Point on Old Grid
Site grid point in terms of O.S. grid:
E = b + E1cos - N1sin
N = a +N1cos - E1sin
Easting E1 N1
Northing
Origin Old Grid  
Origin New Grid b a

5. Whole Circle Bearing (WCB)
North
The angle to a line measured from North in a clockwise direction.
Partials (also known as latitudes and departures) are the East and north vector of the line AB B
WCB
North Partial A
East Partial
East Partial = L x sin(WCB)
North Partial = L x cos(WCB

6. Whole Circle Bearing (WCB) 2
Not measured directly as North is difficult to find (Magnetic, True, Grid?) but by using two reference stations HENCE WCB will be to True or Grid North.
EB, NB
WCB
EA, NA
WCBAB = TAN-1(EB – EA / NB-NA)

7. NORTH?
True or Geographic North – Top of globe, where lines of longtitude meet.
Grid North – Lines parallel to 2 W meridian - in same direction over the drawn map area.
Magnetic North – as indicated by magnetic compass needle. Not at true North and varies in position.

8. NORTH 2
True North
Gyro theodolite which utilises spin of earth for orientation will refer back to this

9. NORTH 3 Grid North – as used on maps
Due to projection of spherical surface onto flat sheet

10. NORTH 4
MAGNETIC NORTH – Position varies seasonally and is away from the true north.
Due to molten iron core of earth.
Geologically evidence that it has flipped over several times.
No reason why it shouldn’t do so again.
Shift documented for navigation purposes.
Angle between Longitudes and Magnetic north depends also on latitude position

11. Cartesian to Polar Conversion
(E, N)  R
R,
The position of any point can be expressed by either cartesian coordinates or by using Polar coordinates.
Cartesian or Rectangular coordinates
Polar coordinates N

12. WCB and POLAR coords  R, WCB R Eastings = L x sin(WCB)
NOTE:
E = R x cos()
N = R x sin()
Eastings = L x sin(WCB)
Northings = L x cos(WCB) N E
Eastings
Northings L

13. Setting out using RADIALS
To set out from B using A as the reference station:
Find Deflection angle 
and Setting out distance L A B  L
Point to be set out
Observation Station
Reference Station

14. Setting out using RADIALS -2B
1. Sketch known points and stake out point correctly relative to each other. Do not try to scale coordinates
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN

15. Setting out using RADIALS -3B
3060
2. Add Coordinate values to axis.
3050
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN
2000
5000
6450
6500

16. Setting out using RADIALS -4
3060 A B
3. Identify Delection angle .
3050
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN
2000
5000
6450
6500

17. Setting out using RADIALS -5
3060 A B
4. Identify components of Delection angle . β
3050
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN α
2000
5000
6450
6500

18. Setting out using RADIALS -6B
5000
6450
6500
3060
3050
2000 α β
5. Identify relevant right angled triangles.
HINT: Start with Hypoteneuse to component deflection angles

19. Setting out using RADIALS -7B
5000
6450
6500
3060
3050
2000 α β
6. Calculate Difference in Eastings and Northings for each triangle
Eref = EB –EA
Nref = NB - NA
EStakeout = EB –E
Estakeout = N –NB
1500
1050 10 50

20. Setting out using RADIALS -8B
5000
6450
6500
3060
3050
2000 α β
7. Calculate components of deflection angles.
 = tan-1 Nref /Eref
 = tan-1 NStakeout /Estakeout
Hence  =  +  10 50
1500
1050

21. Setting out using RADIALS -9
8. Finally calculate the setting out length.
Note that all partials have already been computed
L = (NStakeout2 + Estakeout2)
Best calculated using spreadsheet program.
Facility available on total Station for inputting reference stations and required stake out point – Setting out information calculated automatically ( but how do you check values?)
Consult user manual as each instrument is different