Coordinate systemsCoordinate systemsO.S. GridO.S. Grid

Site GridSite Grid

NorthsNorths

Whole Circle BearingsWhole Circle Bearings

PartialsPartials

Polar ConversionsPolar Conversions

Radial Setting OutRadial Setting Out

Ordnance Survey GridOrdnance 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 accuracyGrid size and accuracy

64772.123mE, 54752.765mN

60 6550

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

OS Grid to Site Grid conversionsOS Grid to Site Grid conversions

Site grid point in terms of O.S. grid:

E = b + E1cos - N1sin

N = a +N1cos - E1sin

abOrigin New Grid

Origin Old Grid

Point on Old Grid

Easting

No

rth

ing

E 1 N1

Whole Circle Bearing (WCB)Whole Circle Bearing (WCB)• 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

A

North

North Partial

East Partial

• East Partial = L x sin(WCB)

• North Partial = L x cos(WCB

WCB

• 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.

EA, NA

WCB

EB, NB

WCBAB = TAN-1(EB – EA / NB-NA)

Whole Circle Bearing (WCB) 2Whole Circle Bearing (WCB) 2

NORTH?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 2NORTH 2

True North

Gyro theodolite which utilises spin of earth for orientation will refer back to this

NORTH 3NORTH 3Grid North – as used on maps

Due to projection of spherical surface onto flat sheet

NORTH 4NORTH 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 ConversionCartesian to Polar Conversion

N

E

(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

WCB and POLAR coordsWCB and POLAR coords

R

R,WCB

NOTE:

E = R x cos()

N = R x sin()

NOTE:

Eastings = L x sin(WCB)

Northings = L x cos(WCB)

N

EEastings

Nor

thin

gs

L

Setting out using RADIALSSetting out using RADIALS

Observation Station

Reference Station

To set out from B using A as the reference station:

Find Deflection angle

and Setting out distance L

A

B

LPoint to be set out

Setting out using RADIALS -2Setting out using RADIALS -2

A

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 -3Setting out using RADIALS -3

A

B

2. Add Coordinate values to axis.

Reference Coordinates:

A: 5000mE, 2000mN

B: 6500mE,3050mN

Stake out Coordinate:

6450mE, 3060mN

3060

3050

20005000 6450 6500

A

B

3. Identify Delection angle .

Reference Coordinates:

A: 5000mE, 2000mN

B: 6500mE,3050mN

Stake out Coordinate:

6450mE, 3060mN

5000 6450 6500

3060

3050

2000

Setting out using RADIALS -4Setting out using RADIALS -4

A

B

4. Identify components of Delection angle .

Reference Coordinates:

A: 5000mE, 2000mN

B: 6500mE,3050mN

Stake out Coordinate:

6450mE, 3060mN

5000 6450 6500

3060

3050

2000

α

β

Setting out using RADIALS -5Setting out using RADIALS -5

A

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 -6Setting out using RADIALS -6

Setting out using RADIALS -7Setting out using RADIALS -7

A

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

1050

Setting out using RADIALS -8Setting out using RADIALS -8

A

B

5000 6450 6500

3060

3050

2000

α

β

7. Calculate components of deflection angles.

= tan-1 Nref /Eref

= tan-1 NStakeout /Estakeout

Hence = +

1500

1050

1050

8. Finally calculate the setting out length.

Note that all partials have already been computed

L = (NStakeout2 + Estakeout

2)

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

Setting out using RADIALS -9Setting out using RADIALS -9