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

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. 64567.123mE, 58945.456mN)

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 64772.123mE, 54752.765mN

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

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

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)

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.

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

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

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

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

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

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

Setting out using RADIALS -2 B 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

Setting out using RADIALS -3 B 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

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

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

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

Setting out using RADIALS -7 B 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

Setting out using RADIALS -8 B 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

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